So the drop-down menu for the server isn't working (I've tried on firefox and chrome) and when I try to enter the server manual (I've tried multiple variations of synirc and synirc webirc) I get a "Could not resolve host name".

I've never encountered a problem like this logging onto our chat. Any suggestions?

I've seen that happen before with mibbet; it seems to be a weird glitch that happens every now and then. In the meantime, try using the built-in widget in the chat guide: http://www.scp-wiki.net/chat-guide